Some Topics in Reactor Kinetics Page: 1 of 21
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Second United Nations A/CNF.15/P/629
International Conference Abstract (USA)
7 March 1958
L4 on the Peaceful Uses
of Atmic EergyORIGINALS ENGLISH
Confidential until official release during Conference
A SURVEY OF NUCLEAR REACTOR KINETICS
E. R. Cohen, D. L. Hetrick and W. A. Horning
The Boltzmann equation for the neutron distribution in a
reactor is first reduced to the energy independent, space dependent
equation in terms of neutron importance functions. It is therefore
possible to obtain equivalent "one-group" neutron models which are more
general than the simple "thermal group" approximation. The one group
space dependent equation can then be used to investigate the effects of
spatially localized perturbations. In particular, the "rod-drop" method
of determining control rod worth is discussed in general terms as an ex-
ample of such spatially localized perturbations. The conditions for sta-
bility of a reactor against flux oscillations initiated by spatially
localized perturbations are also investigated.
The equations are then reduced to space and energy independent
form and several cases are presented for which analytic solutions are
possible. In general, however, the feedback of the power and temperature
variables alter the reactivity and introduce non-linear terms into the
equations and no analytic solutions exist. In such cases numerical
methods must be used. Several methods present themselves. There are
various possible numerical procedures based upon the replacement of the
differential equations by difference equations and the advantages and
disadvantages of these are reviewed. An alternative approach which can
be quite useful takes as its starting point the formulation of the system
as a set of coupled integral equations and the numerical replacement of
integrals by approximating.sums. In all of these methods the problems of
convergence and numerical stability are important, and the methods for
formulating convergence and stability criteria are discussed.
In reactor transients in which the reactor is self-limiting,
the nature of the feedback mechanism is of utmost importance. The types
of feedback mechanisms which are present in homogeneous solution reactors
(KEWB) and in plate-type -reactors (SPERT, OMRE, EBWR) are discussed and
certain general stability criteria are evaluated. The general results
are illustrated with data on the performance of the SPERT and KEWB tests.
In the aqueous homogeneous reactor, two reactivity feedback
mechanisms may be distinguished: a prompt negative temperature coef-
ficient arising primarily from thermal expansion of the fuel solution,
and a delayed negative void coefficient resulting from the formation of
bubbles of radiolytic decomposition gas. Data from the Kinetic Experi-
ment Water Boiler are present, together with a discussion of various
mathematical models which have been used to simulate the dynamic behavior
of this reactor.
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Cohen, E. R. Some Topics in Reactor Kinetics, report, October 31, 1958; Canoga Park, California. (https://digital.library.unt.edu/ark:/67531/metadc1020452/m1/1/: accessed March 22, 2019), University of North Texas Libraries, Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.